Question

You took a 30-year half-million-dollar mortgage at 3% per year. What percent of your last payment goes to reduce principal?

Answer 1

Particulars	Amount
Loan Amount	$           500,000.00
Int rate per Anum	3.0000%
No. of Years	30

Annual Instalemnt = Loan Amount / PVAF (r%, n)  
Where r is Int rate per Anum & n is No. of Years  
= $ 500000 / PVAF (0.03 , 30)  
= $ 500000 / 19.6004  
= $ 25509.63  

Equal annual payment = $ 25509.63  
PVAF = [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.03)^-30]] /0.03
= [ 1 - [(1.03)^-30]] /0.03
= [ 1 - [0.41199]] /0.03
= [0.58801]] /0.03
= 9.6004

Last payment = $ 25509.63 , this includes the interest portion also .

interest = $ 25509.63 *( 3% / 103%) = $ 743

Principal amount = $ 25509.63 - $ 743 = $ 24766.63  

% of principal payment = $ 24766.63 / $ 25509.63 = 0.97087 or 97.087 %

or it is in simple calculation

in total payment of 103 % principal portion is 100 % ( 103 % - interest 3 %)

so % of principal payment = 100 % / 103 % = 0.97087 or 97.087 %